Titlebook: An Introduction to Delay Differential Equations with Applications to the Life Sciences; Hal Smith Textbook 2011 Springer Science+Business

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Phage and Bacteria in a Chemostat,e assumption of a fixed latent period for virus inside the infected cell. The main biological issues addressed are the persistence and extinction of bacteria and of bacteriophage(phage). From a mathematical perspective, we focus on bifurcation of equilibria and Hopf bifurcation from the coexistence equilibrium.

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Hal SmithFocuses on key tools to understand delay equations.Begins with a survey of mathematical models involving delay equations.Wealth of examples, exercises and illustrations.Includes supplementary material

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https://doi.org/10.1007/978-3-322-84159-9 application area, in order to motivate our study of delay differential equations. These range from models in population biology, physiology, epidemiology, economics,and neural networks, to control of mechanical systems. Some of these are treated in detail later in the text; others can serve as pote

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https://doi.org/10.1007/978-3-322-84159-9ts. More general delay equations require a more general framework for existence and uniqueness.This includes some peculiar notation endemic to the subject and the identification of the appropriate state space for delay equations. Solutions either extend to the entire half–line or blowup in finite ti

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https://doi.org/10.1007/978-3-663-01721-9 the system about the equilibrium and to determine exponential rates of growth and decay for the associated linear system. The framework for carrying this out is taken up in this chapter. Although the method is similar to that for ODEs, the characteristic equation is more complicated, typically havi

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Wiedereröffnung der Stadthalle Wuppertalously establishing the existence of periodic solutions. We begin with an example where the bifurcation can be easily calculated in order to show key features of a Hopf bifurcation.Then the theorem is stated without proof along with a discussion of the stability properties of bifurcating periodic sol